Regarding the
SEAT Ibiza i-Tech Mk5 model, this was a limited edition for roughly 2 years from mid 2013 to mid 2015, they only came with the one engine in this model, 1.2 TSi (EA111) engine code CBZB which has timing chain.
Also this engine I think had the upgraded timing chain & tensioner from 2013 onwards, due to the
Ibiza before 2013 or 2012 having a thinner chain & weaker tensioner that was suspected of failing, between 40k miles (70,000km) & 50k miles (80,000km)
It's important to carry out regular oil changes on the i-Tech 1.2 TSi engine, but even more so if you've purchased the car with out full history.
The standard air filter box is normally situated just behind the battery, close to bulkhead just in front of the ECU on the left side, I thought it might have a air flow sensor attached to OEM air box, but I don't think it has.
On the SEAT ETKA parts site it list's this part number twice 03G 906 051D for MAP sensor and boost pressure sensor.
Basically this one sensor is used / fitted in two places on your engine.
03G 906 051D
MAP sensor is Mass Air Pressure sensor measures the volume of air in inlet manifold.
03G 906 051D
Boost pressure sensor measures the turbo boost air pressure traveling down turbo outlet boost pipe to intercooler.
As there's no air flow sensor fitted to standard air filter box, your engine should run fine with the induction filter kit fitted.
But as you've got no service history with car only MOT certs, you don't know if the ECU has been remapped, which sometimes can cause issues in the future a year or two down the line so to speak.
As Swanbon has said I'd get the original OEM air filter box fitted back on, and see if that makes a difference, I don't think it will, but the garage has told you they think it's causing your issue ??
Get them to put it back to standard especially if you've got any warranty with the car ?
Can you hear any rattling noise when you first start up your car from cold, it's rare for the later 1.2 TSi engines to have timing chain issues, as it should have the upgraded chain & tensioner, but there's still a small risk.
Symptoms were on the older car's before 2013, rattling noise on cold start ups, valve timing can be slightly out causing poor starting or running issues, it has been known for later car's 2013 onwards to have this, but is rare.
Hope this helps
Si